1. Field of the Invention
The present invention relates to a QR decomposition apparatus and method for a Multiple Input Multiple Output (MIMO) system; and, more particularly, to an QR decomposition apparatus and method for improving performance with computation complexity reduced in an Orthogonal Frequency Division Multiplexing (OFDM) MIMO system.
This work was supported by the IT R&D program of MIC/IITA [2006-S-002-02, “IMT-Advanced Radio Transmission Technology with Low Mobility”].
2. Description of Related Art
It is a requirement of a wireless communication system to transmit a large amount of high quality multimedia data using a limited frequency. As a method for transmitting a large amount of data using a limited frequency, a Multiple Input Multiple Output (MIMO) system was introduced. The MIMO system forms a plural of independent fading channels using multiple antennas at receiving and transmitting ends and transmits different signals through each of multiple transmission antennas, thereby significantly increasing a data transmission rate. Accordingly, the MIMO system can transmit a great deal of data without expansion of a frequency.
However, the MIMO system has a shortcoming that the MIMO system is weak to inter-symbol interference (ISI) and frequency selective fading. In order to overcome the shortcoming, an Orthogonal Frequency Division Multiplexing (OFDM) scheme was used. The OFDM scheme is a modulation scheme most appropriate for transmitting data at a high speed. The OFDM scheme transmits one data row through a subcarrier having a low data transmission rate.
A channel environment for wireless communication has multiple paths due to obstacles such as a building. In a wireless channel environment having multi-paths, delay spread occurs due to the multiple paths. If delay spread time is longer than a symbol transmission interval, inter-symbol interference is caused. In this case, frequency selective fading occurs in a frequency domain. In case of using a single carrier, an equalizer is used to remove the ISI. However, complexity of the equalizer increases as a data transmission rate increases.
The shortcomings of the MIMO system can be attenuated using an Orthogonal Frequency Division Multiplexing (OFDM) technology. In order to overcome the shortcomings of the MIMO system while maintaining the advantages of the MIMO system, an OFDM technology was applied to a MIMO system having N transmission antennas and N reception antennas. That is, a MIMO-OFDM system was introduced.
FIGS. 1A and 1B are block diagrams schematically illustrating an MIMO OFDM system. FIG. 1A is a block diagram of a transmitting end in the MIMO-OFDM system, and FIG. 2 is a block diagram of a receiving end in the MIMO-OFDM system.
Referring to FIG. 1A, the transmitting side includes a serial-to-parallel (S/P) converter, a plurality of encoders 102, a plurality of Quadrature Amplitude Modulation (QAM) mappers 103, a plurality of Inverse Fast Fourier Transform (IFFT) units 104, a plurality of cyclic prefix (CP) inserters 105, and digital-to-analog conversion (DAC) and radio frequency (RF) unit 106. The S/P converter divides transmission data into a plurality of data rows before encoding the transmission data.
The encoders 102 encode the data rows, respectively. After encoding, the QAM mappers 103 modulate the encoded data rows based on a predetermined modulation scheme such as Binary Phase Shift Keying (BPSK), Quadrature Phase Shift Keying (QPSK), 16 QAM, and 64 QAM. The IFFT units 104 transform the modulated symbols into time domain signals, respectively. The CP inserters 105 insert a CP code for a guard interval into the time domain signals. Then, the DAC & RF unit 106 convert the CP inserted digital signals to analog signals and covert the analog signals to RF signals. The RF signals are transmitted through an antenna.
Referring to FIG. 1B, the receiving part includes a plurality of analog-to-digital conversion (ADC) and RF units 107, a plurality of CP removers 108, a plurality of Fast Fourier Transform (FFT) units 109, an MIMO receiver, a plurality of decoders 111, and a parallel-to-serial (P/S) converter 112. The ADC & RF units 107 convert RF signals into analog signals and convert the analog signals into digital signals. The CP removers 108 remove CP codes which were inserted for a guard interval and transfer the CP code-removed signals to the FFT units 109.
The FFT units 109 perform FFT on the input parallel signals which are the CP removed signals. The MIMO receiver 110 estimates transmission data symbols which are generated by FFT. The MIMO receiver 110 calculates a log likelihood ratio (LLR) from the estimated symbols. The decoders 111 decode data rows transferred from the MIMO receiver 110 and estimate the transmission data, respectively. The of P/S converters 112 convert parallel data modulated by each decoder 111 into serial data.
The MIMO receiver 110 generally uses a decision feedback equalizer (DFE), zero forcing (ZF), minimum mean square error estimation (MMSE), and bell labs layered space-time (BLAST).
In the MIMO wireless communication system, each of the signals transmitted through a plurality of antennas is received with the influence of individual channel. A received signal r of a predetermined subcarrier may be expressed as Eq. 1.r=Hx+n  Eq. 1
In Eq. 1, r is a received signal vector
  r  =            [                                                  r              0                                                                          r              1                                                                          r              2                                                            ⋮                                                              r              n                                          ]        .  
In general, the number of antennas for receiving a signal is equal to or larger than the number of antennas for transmitting a signal. A channel matrix H is a matrix formed of a wireless channel between antennas for transmission and antennas for reception. The channel matrix H is shown below. Here, the number of antennas for receiving a signal is n+1, and the number of antennas for transmitting a signal is m+1.
  H  =      [                                        h                          0              ,              0                                                            h                          0              ,              1                                                            h                          0              ,              2                                                            h                          0              ,              3                                                …                                      h                          0              ,              M                                                                        h                          1              ,              0                                                            h                          1              ,              1                                                            h                          1              ,              2                                                            h                          1              ,              3                                                …                                      h                          1              ,              M                                                                        h                          2              ,              0                                                            h                          2              ,              1                                                            h                          2              ,              2                                                            h                          2              ,              3                                                …                                      h                          2              ,              M                                                                        h                          3              ,              0                                                            h                          3              ,              1                                                            h                          3              ,              2                                                            h                          3              ,              3                                                …                                      h                          3              ,              M                                                            ⋮                          ⋮                          ⋮                          ⋮                          ⋰                          ⋮                                                  h                          n              ,              0                                                            h                          n              ,              1                                                            h                          n              ,              2                                                            h                          n              ,              3                                                …                                      h                          n              ,              m                                            ]  
X is a transmitted signal vector and expressed as
      x    =          [                                                  x              0                                                                          x              1                                                            ⋮                                                              x              m                                          ]        ,and n is a noise signal of an antenna for receiving a signal and expressed as
  n  =            [                                                  n              0                                                                          n              1                                                                          n              2                                                            ⋮                                                              n              n                                          ]        .  
QR decomposition for the channel matrix H can be expressed as Eq. 2.
                                                        R              =              0                        ,                          Q              =              H                                ⁢                                          ⁢                                                    for                ⁢                                                                  ⁢                i                            =              1                        ,            …            ⁢                                                  ,                          n              T                                ⁢                                          ⁢                                          ⁢                                    norm              i                        =                                                                            q                  i                                                            2                                ⁢                                          ⁢          end          ⁢                                          ⁢                                                    for                ⁢                                                                  ⁢                i                            =              1                        ,            …            ⁢                                                  ,                          n              T                                ⁢                                          ⁢                                          ⁢                                    r                              i                ,                i                                      =                                          norm                i                                              ⁢                                          ⁢                                          ⁢                                    q              i                        :=                                          q                i                            /                              r                                  i                  ,                  i                                                                    ⁢                                  ⁢                                  ⁢                                            for              ⁢                                                          ⁢              k                        =                          i              +              1                                ,          …          ⁢                                          ,                      n            T                          ⁢                                  ⁢                                  ⁢                              r                          i              ,              k                                =                                    q              i              H                        ·                          q              k                                      ⁢                                  ⁢                                  ⁢                              q            k                    :=                                    q              k                        -                                          r                                  i                  ,                  k                                            ·                              q                i                                                    ⁢                                  ⁢                                  ⁢                              norm            k                    :=                                    norm              k                        -                          r                              i                ,                k                            2                                      ⁢                                  ⁢                                  ⁢        end        ⁢                                  ⁢        end                            Eq        .                                  ⁢        2            
After QR decomposition, the received signal can be expressed as Eq. 3.r=QRx+n  Eq. 3
In Eq. 3, Q is a unitary matrix (QHQ=I), and expressed as follows.
  Q  =      [                                        q                          0              ,              0                                                            q                          0              ,              1                                                            q                          0              ,              2                                                            q                          0              ,              3                                                …                                      q                          0              ,              n                                                                        q                          1              ,              0                                                            q                          1              ,              1                                                            q                          1              ,              2                                                            q                          1              ,              3                                                …                                      q                          1              ,              n                                                                        q                          2              ,              0                                                            q                          2              ,              1                                                            q                          2              ,              2                                                            q                          2              ,              3                                                …                                      q                          2              ,              n                                                                        q                          3              ,              0                                                            q                          3              ,              1                                                            q                          3              ,              2                                                            q                          3              ,              3                                                …                                      q                          3              ,              n                                                            ⋮                          ⋮                          ⋮                          ⋮                          ⋰                          ⋮                                                  q                          n              ,              0                                                            q                          n              ,              1                                                            q                          n              ,              2                                                            q                          n              ,              3                                                …                                      q                          n              ,              n                                            ]  
R denotes an upper triangular matrix and is expressed as follows.
  R  =      [                                        r                          0              ,              0                                                            r                          0              ,              1                                                …                                      r                          0              ,              m                                                            0                                      r                          1              ,              1                                                …                                      r                          1              ,              m                                                            ⋮                          ⋮                          ⋰                          ⋮                                      0                          0                          …                                      r                          m              ,              m                                                            0                          0                          …                          0                                      ⋮                          ⋮                          ⋰                          ⋮                                                  0                          n              ,              0                                                            0                          n              ,              1                                                …                                      0                          n              ,              m                                            ]  
A new received signal vector y can be expressed as Eq. 4.
                    y        =                                            Q              H                        ⁢            r                    =                                                                      Q                  H                                ⁢                QRx                            +                                                Q                  H                                ⁢                n                                      =                                          Rx                +                                                      n                    ~                                    ⁢                                                                          [                                                                                                              y                          0                                                                                                                                                              y                          1                                                                                                                                                              y                          2                                                                                                                                                              y                          3                                                                                                                                    ⋮                                                                                                                                      y                          n                                                                                                      ]                                            =                                                                    [                                                                                                                        r                            00                                                                                                                                r                            01                                                                                                                                r                            02                                                                                                                                r                            03                                                                                                    …                                                                                                      r                                                          0                              ⁢                              n                                                                                                                                                                            0                                                                                                      r                            11                                                                                                                                r                            12                                                                                                                                r                            13                                                                                                    …                                                                                                      r                                                          1                              ⁢                              n                                                                                                                                                                            0                                                                          0                                                                                                      r                            22                                                                                                                                r                            23                                                                                                    …                                                                                                      r                                                          2                              ⁢                              n                                                                                                                                                                            0                                                                          0                                                                          0                                                                                                      r                            33                                                                                                    …                                                                                                      r                                                          3                              ⁢                              n                                                                                                                                                                            ⋮                                                                          ⋮                                                                          ⋮                                                                          ⋮                                                                          ⋰                                                                          ⋮                                                                                                                      0                                                                          0                                                                          0                                                                          0                                                                          …                                                                                                      r                            mn                                                                                                                ]                                    ⁡                                      [                                                                                                                        x                            0                                                                                                                                                                            x                            1                                                                                                                                                                            x                            2                                                                                                                                                                            x                            3                                                                                                                                                ⋮                                                                                                                                                  x                            n                                                                                                                ]                                                  +                                  [                                                                                                                                          n                            ~                                                    0                                                                                                                                                                                          n                            ~                                                    1                                                                                                                                                                                          n                            ~                                                    2                                                                                                                                                                                          n                            ~                                                    3                                                                                                                                    ⋮                                                                                                                                                                  n                            ~                                                    n                                                                                                      ]                                                                                        Eq        .                                  ⁢        4            
Since the received signal y is expressed as multiplication of the upper triangular matrix R and the transmitted signal x in Eq. 4, computation amount is considerably reduced for restoring a received signal. However, the described QR decomposition method may have a problem in that computation amount significantly increases for decomposing a channel H if the number of antennas constantly as seen in Eq. 2. That is, a hardware structure becomes complicated because the number of multipliers increases, and computation complexity also increases.